Need to get to Mljet from Brac / Split

Our plans are to be on Brac form Sept 3-4. Then we would like to spend the evening of Sept 4 on Mljet before continuing on to Dubrovnik. We are willing to take a couple of ferries to get to Mljet, but I’m having a lot of difficulty in figuring out how to do this. Can we go through Hvar?

Just looking at Google Maps to see the best way to get from Brac/Split to Mljet and it is suggesting that I take the Suartin-Makarska ferry back to mainland, the Ploce-Trpanj ferry, and one other ferry that I can’t find anywhere.

I appears that the departure port is Trstenik (into Polace). Any idea what company runs this ferry?